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# What is the equivalent resistance between a and b in given figure

Samyak Jain
333 Points
2 years ago
Clearly, 15 $\dpi{80} \Omega$ and 10 $\dpi{80} \Omega$ resistors are in series since same current flows through them.
Similarly, 20 $\dpi{80} \Omega$ and 30 $\dpi{80} \Omega$ are in series and 40 $\dpi{80} \Omega$ 10 $\dpi{80} \Omega$ are in series.
Equivalent series resistance of 15 $\dpi{80} \Omega$ and 10 $\dpi{80} \Omega$ is (15 + 10) = 25 $\dpi{80} \Omega$, that of 20 $\dpi{80} \Omega$ and 30 $\dpi{80} \Omega$ is 50 $\dpi{80} \Omega$
and that of 40 $\dpi{80} \Omega$ and 10 $\dpi{80} \Omega$ is 50 $\dpi{80} \Omega$.
Take a point D between 2 $\dpi{80} \Omega$ and 5 $\dpi{80} \Omega$ whose potential is VD. Since the potential across a connecting wire
is same, potential of a point between 40 $\dpi{80} \Omega$ and 30 $\dpi{80} \Omega$ is also VD. Now, take a point C between two 10 $\dpi{80} \Omega$ resistors
whose potential is VC, which is also the potential of a point between 8 $\dpi{80} \Omega$ and 20 $\dpi{80} \Omega$.
In short, potential difference between equivalent series resistance of 15 $\dpi{80} \Omega$ and 10 $\dpi{80} \Omega$ (25 $\dpi{80} \Omega$), between
equivalent series resistance of 40 $\dpi{80} \Omega$ and 10 $\dpi{80} \Omega$ (50 $\dpi{80} \Omega$) and between equivalent series resistance of
20 $\dpi{80} \Omega$ and 30 $\dpi{80} \Omega$ (50 $\dpi{80} \Omega$) is same and is |VC – VD| i.e.
25 $\dpi{80} \Omega$, 50 $\dpi{80} \Omega$ and 50 $\dpi{80} \Omega$ resistors are in parallel whose equivalent resistance is
1/(1/25 + 1/50 + 1/50) $\dpi{80} \Omega$ =  1/{(2 + 1 + 1)/50} $\dpi{80} \Omega$ =  50 / 4 $\dpi{80} \Omega$ = 25/2 $\dpi{80} \Omega$.
This 25/2 $\dpi{80} \Omega$ resistance is in series with 2 $\dpi{80} \Omega$ and 8 $\dpi{80} \Omega$ resistors.
$\therefore$ The equivalent resistance between points A and B is (25/2 + 2 + 8) $\dpi{80} \Omega$ = 45/2 $\dpi{80} \Omega$.